Internal problem ID [15485]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 18.2. Expanding a solution in generalized power
series. Bessels equation. Exercises page 177
Problem number: 741.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
\[ \boxed {9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
Order:=6; dsolve(9*x*(1-x)*diff(y(x),x$2)-12*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
\[ y = c_{1} x^{\frac {7}{3}} \left (1+\frac {4}{5} x +\frac {44}{65} x^{2}+\frac {77}{130} x^{3}+\frac {1309}{2470} x^{4}+\frac {119}{247} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (1+\frac {1}{3} x +\frac {2}{9} x^{2}+\frac {14}{81} x^{3}+\frac {35}{243} x^{4}+\frac {91}{729} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 85
AsymptoticDSolveValue[9*x*(1-x)*y''[x]-12*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {91 x^5}{729}+\frac {35 x^4}{243}+\frac {14 x^3}{81}+\frac {2 x^2}{9}+\frac {x}{3}+1\right )+c_1 \left (\frac {119 x^5}{247}+\frac {1309 x^4}{2470}+\frac {77 x^3}{130}+\frac {44 x^2}{65}+\frac {4 x}{5}+1\right ) x^{7/3} \]